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Dafna1 [17]
3 years ago
8

A rectangular pyramid is sliced so the cross section is perpendicular to its base but does not pass through its vertex. What is

the shape of the cross section? trapezoid triangle rectangle square
Mathematics
1 answer:
Dvinal [7]3 years ago
6 0

Answer:  a) trapezoid

<u>Step-by-step explanation:</u>

Since it does not pass through the vertex, it will be a triangle with its tip cut off (aka trapezoid).

Cross section through the vertex is a triangle.

Cross section parallel to the base is a rectangle.

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The Oregon Department of Health web site provides information on the cost-to-charge ratio (the percentage of billed charges that
Alekssandra [29.7K]

Answer:

We conclude that the mean cost-to-charge ratio for Oregon hospitals is lower for outpatient care than for inpatient care.

Step-by-step explanation:W

We are given with the cost-to-charge ratios for both inpatient and outpatient care in 2002 for a sample of six hospitals in Oregon below;

Hospital       2002 Inpatient Ratio         2002 Outpatient Ratio

    1                           68                                            54

    2                          100                                           75

    3                           71                                             53

    4                           74                                            56

    5                          100                                           74

    6                           83                                            71

Let \mu_1 = <u><em>mean cost-to-charge ratio for outpatient care</em></u>

\mu_2 = <u><em>mean cost-to-charge ratio for impatient care</em></u>.

SO, Null Hypothesis, H_0 : \mu_1 \geq \mu_2     {means that the mean cost-to-charge ratio for Oregon hospitals is higher or equal for outpatient care than for inpatient care}

Alternate Hypothesis, H_A : \mu_1 < \mu_2     {means that the mean cost-to-charge ratio for Oregon hospitals is lower for outpatient care than for inpatient care}

The test statistics that would be used here is <u>Two-sample t-test statistics</u> because we don't know about population standard deviations;

                         T.S. =  \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t__n__1_+_n_2_-_2

where, \bar X_1 = sample mean cost-to-charge Outpatient Ratio = \frac{\sum X_1}{n_1} = 63.83

\bar X_2 = sample mean cost-to-charge Impatient Ratio = \frac{\sum X_2}{n_2} = 82.67

s_1 = sample standard deviation for Outpatient Ratio = \sqrt{\frac{\sum (X_1-\bar X_1 )^{2} }{n_1-1} } = 10.53

s_2 = sample standard deviation for Impatient Ratio = \sqrt{\frac{\sum (X_2-\bar X_2 )^{2} }{n_2-1} } = 14.33

n_1 = sample of hospital for outpatient care = 6

n_2 = sample of hospital for outpatient care = 6

Also, s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2}  }{n_1+n_2-2} } =  \sqrt{\frac{(6-1)\times 10.53^{2}+(6-1)\times 14.33^{2}  }{6+6-2} } = 12.574

So, <u><em>the test statistics</em></u>  =  \frac{(63.83-82.67)-(0)}{12.574 \times \sqrt{\frac{1}{6}+\frac{1}{6}  } }  ~ t_1_0

                                     =  -2.595

The value of t test statistics is -2.595.

<u>Now, at 5% significance level, the t table gives critical value of -1.812 at 10 degree of freedom for left-tailed test.</u>

Since, our test statistics is less than the critical value of t as -2.595 < -1.812, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.

Therefore, we conclude that the mean cost-to-charge ratio for Oregon hospitals is lower for outpatient care than for inpatient care.

8 0
4 years ago
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